关于分配格上矩阵方程的一个注记  

A Note on the Matrix Equations In a Distributive Lattice

作　　者：赵萃魁[1] 

机构地区：[1]内蒙古大学数学系

出　　处：《内蒙古大学学报（自然科学版）》1989年第4期446-451,共6页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自治区科学基金

摘　　要：设L是一个分配格,L的每个元素都有有限的并既约分解。在此条件下,本文给出了L上矩阵方程AX=B的全体解的求法,这大大减弱了文[1]中的条件。Let L be a distributive lattice with the property that every element of L has a finite jion-decomposition into joint irreducible elements. Matrix equations of the form AX=B are considered in the lattice L, where A=(a_(ij))_(m×n), B=(b_1,…,b_m)~T, a_(ij), b_i∈L. Necessary and sufficient conditions for the solvability of the equations are obtained. In the solvable case, the entire solution set are determined. This paper weakens the conditions of paper [1]. In paper [1], we require that the lattice L is a Brouwerian lattic and every element of L has a finite jion—decomposition into joint irreducible elements, but in this paper we only require the last one.

关 键 词：分配格 矩阵方程 全体解集 理想格 

分 类 号：O153.1[理学—数学]